Find the seventh term of the arithmetic sequence.

01 / Standard#Your turn

2S_3^2=3S_2S_4,\quad a_1=4

Official paper · jm01-2025 · I.13 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express S₂,S₃,S₄ using the common difference.

Hint 2

The quadratic terms cancel when expanded.

Worked solution

Write and substitute the three sums.
$S_2=8+d,\quad S_3=12+3d,\quad S_4=16+6d$
Solve for d and use the seventh-term formula.
$2(12+3d)^2=3(8+d)(16+6d)\implies d=-2,\quad a_7=4+6d=-8$

B: −8.

Checks and common pitfalls: S₃² means the square of the third partial sum.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write and substitute the three sums.
$S_2=8+d,\quad S_3=12+3d,\quad S_4=16+6d$
Solve for d and use the seventh-term formula.
$2(12+3d)^2=3(8+d)(16+6d)\implies d=-2,\quad a_7=4+6d=-8$

Think first. Reveal a hint when the class is ready.

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